MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
19)
**Find the indicated probability.** 80% of U.S. drivers over the age of 30 have had a speeding ticket and 55% of those have also been in an accident while behind the wheel. What is the probability that a randomly selected U.S. driver over the age of 30 has had a speeding ticket and also been in an accident while behind the wheel? - ○ 0.64 - ○ 0.6875 - ○ 0.3025 - ○ 0.25 - ○ 0.44 **Solution Explanation:** To find the probability, we multiply the probability of each independent event. Let \( A \) be the event "having a speeding ticket," and \( B \) be the event "been in an accident." Given, - \( P(A) = 0.80 \) - \( P(B|A) = 0.55 \) We want to find \( P(A \cap B) \), which is \( P(A) \times P(B|A) \). Calculating: \[ P(A \cap B) = 0.80 \times 0.55 = 0.44 \] Thus, the probability that a randomly selected U.S. driver over the age of 30 has had a speeding ticket and also been in an accident while behind the wheel is **0.44**.
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Transcribed Image Text:**Find the indicated probability.** 80% of U.S. drivers over the age of 30 have had a speeding ticket and 55% of those have also been in an accident while behind the wheel. What is the probability that a randomly selected U.S. driver over the age of 30 has had a speeding ticket and also been in an accident while behind the wheel? - ○ 0.64 - ○ 0.6875 - ○ 0.3025 - ○ 0.25 - ○ 0.44 **Solution Explanation:** To find the probability, we multiply the probability of each independent event. Let \( A \) be the event "having a speeding ticket," and \( B \) be the event "been in an accident." Given, - \( P(A) = 0.80 \) - \( P(B|A) = 0.55 \) We want to find \( P(A \cap B) \), which is \( P(A) \times P(B|A) \). Calculating: \[ P(A \cap B) = 0.80 \times 0.55 = 0.44 \] Thus, the probability that a randomly selected U.S. driver over the age of 30 has had a speeding ticket and also been in an accident while behind the wheel is **0.44**.
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